satisfying \(y(0)=x\) . Further, even if \(p\le d\) , then a solution to the latter ODE may be not unique for a.e. initial datum,
but in this case there is a natural selection of such solutions called regular Lagrangian flow [1]}.
Moreover, there are many other cases besides Sobolev regularity when the vector field \(V\)  admits a regular Lagrangian flow.
In view of the Rampazzo-Sussmann result for Lipschitz vector fields, it is tempting to conjecture that also in the cases
in which the fields \(V^i\in W^{1,p_i}(\mathbb {R}^d;\mathbb {R}^d)\)  generating unique flows for a.e. initial datum (or at least regular Lagrangian flows)
\(F^i\) , it is true that
\(F_t^1(F_s^2(x))= F_s^2(F_t^1(x))\quad \mbox{for a.e. $x\in \mathbb {R}^d$, whenever } [V^1, V^2] = 0 \quad \mbox{a.e.},\) 
